Отыскать производные функций, заданных в явном и неявном виде. а) y=(1+(x-1)/(x+1))^sqrt(2+x^2);

f(x) = ((-1 / 5) *x^3 + 45x^2 + 4x 1) = ((-1 / 5) * x^3) + (45x^2) + (4x) (1) =

(-1 / 5) * 3 * x^2 + 45 * 2 * x + 4 0 = (-3 / 5) * x^2 + 90x + 4.

y = ((cos^2 x) * (1 / x)) = (cos^2 x) * (1 / x) + (cos^2 x) * (1 / x) = (cos x) * (cos^2 x) * (1 / x) + (cos^2 x) * (1 / x) = (-2 * (sin x) * (cos x) * (1 / x)) + (cos^2 x) * (-1 / x^2) = (-2(sin x)(cos x) / x) + (cos^2 x / x^2).

f(x) = ((x^2 + 1)^-(1 / 2)) = (x^2 + 1) * ((x^2 + 1)^(-1 / 2)) = ((x^2) + (1)) * ((x^2 + 1)^(-1 / 2)) = 2x * (1 / 2) * (x^2 + 1)^(-3 / 2) = x / ((x^2 + 1)^(3 / 2)) = x / ((x^2 + 1)^3).

y = (x^2 * ln (tg 2x)) = (x^2) * ln (tg 2x) + x^2 * (ln (tg 2x)) = (x^2) * ln (tg 2x) + x^2 * (tg 2x) * (ln (tg 2x)) = (x^2) * ln (tg 2x) + x^2 * (2x) * (tg 2x) * (ln (tg 2x)) = 2 * x^(2 1) * ln (tg 2x) + x^2 * 2 * (1 / (cos^2 2x) * (1 / (tg 2x)) = 2xln (tg 2x) + (2x^2 / (cos^2 2x)(tg 2x)).